Ok, I've finally understood your points here. You're right. Maybe I'm too strict when it comes to consider Socionics rules/information. So, can I ask you (besides what you've already written) what makes you think I'm an LII. I feel like I always need more information. Since you are an LII yourself, it would be great if you shared your thoughts abut what we have in common, at least on a superficial level.
I am glad that we can come to terms. I am sorry if I sounded rude at any point or caused offense. I understand how frustrating it can be to be uncertain of your type. As I said, I was uncertain for many years. It is a difficult subject, with a great deal of room for different possibilities due to the subjectivity of the system.
I believe you could be either an ILI or a LII. At least, I am fairly certain you are one of these two types. I lean towards LII because the overall tone of your OP seems LII. You used the term "analytical" many times, as well as "mathematics", both of these are typically associated with favoring Ti. However, there are discrepancies. You pointed out a few, for example when you quoted me and mentioned that you can't stand incompetence and you don't care what people think about you. It is true, these show you do not value Fe very much if at all, and might value Te as a creative function. There is the possibility of this leading to an ILI type conclusion.
Some people responded with very good observations about your feelings as shown in your OP. There seemed to be a consensus for ILI as a type conclusion, and that may be the way to go for now. I confess, I am not good at reading people's feelings or understanding their emotions, and you would be the best judge of your own feelings anyway. It is simply in my nature to always play devil's advocate for contrarian opinions, whenever I see everyone agreeing on a specific thing. I like to consider every point of view, and deconstruct a conclusion by analysis into only what is explicitly true, followed by what is implicitly true given the explicit facts, and then typically this leaves room for a variety of possible interpretations of the data, and as a result, I cannot come to any conclusion. Thus, I abstain from most topics.
Perhaps the above paragraph is also helpful to you in understanding what type you might be? If you find you have the same approach, you could be an LII like me. You can see how, because I am
so rigorous in my analysis and logic, my standards are so demanding that I cannot form a conclusion, and thus, my expressive function/creative function is to offer up many possibilities and suggestions, and to encourage further investigation. This is how I was able to finally decide on my own type being LII (Ti lead, Ne creative).
If instead, you find that you tend to express only your opinions and conclusions, and you are drawn to create decisive final
answers to things, you can see how that would indicate your creative function is Te - especially if you like those conclusions to be practical, competent, and based on solid facts. Especially if you tend see many possibilities, but keep them private to yourself rather than offering them up for consideration, you can perhaps see how that might show a lead Ni function, because your intuitive perspective is kept introverted.
I do not know you very well so it is up to you, but if it were me, I would look at the situation that way, asking myself how I tend to create, and what I tend to create in the world around me. In my personal experience and throughout my study I have found that when taking a function-based approach to understanding a person's type, it is always the first two functions that are the most obvious - and in socionics especially, I find the creative function is probably the most clear indicator of a person's type.